How do you find the common ratio, r, for the geometric sequence that has a1 =100 and a8 =50?

1 Answer
sente
Feb 27, 2016

#r = (1/2)^(1/7)~~0.9057#

Explanation:

The key to solving this problem is in recognizing what the terms of a geometric sequence look like. If we write a geometric sequence in its most general form, we have:

#a_1 = a_1#
#a_2 = a_1r#
#a_3 = a_1r^2#
...
#a_n = a_1r^(n-1)#

In this case #a_8 = 50#. But, using #a_1 = 100#, we have

#50 = a_8 = a_1r^(8-1) = 100r^7#

#=>r^7 = 50/100 = 1/2#

#:.r = (1/2)^(1/7)~~0.9057#

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